idea_to_try.sf

#!/usr/bin/ruby

# Idea: for each number `n` in `arr` and for each lambda `l` in `arr`, replace large prime factors of `l` with other prime divisors from lambda `l`.

var arr = [
 487954732492026166035814706202314376705
 141934960805533535384100259905
 2609668563371076823446624111609234945
 22321294006753093794484119100782564881584237146952694846489144434824034305
 72148620605333310080719701812041760839024918297692839329815300886091224428394819515628545
 967037403232220731074074563038316755517610240570658812669537184604036430235566311331012838883641380865
 406402829025353014759868508514893182061635216385
 15076244937897319383799036175429336548625369631595367899653198961989759434810928251355411574785
 871005264581548962932418919531990803260747265
 610012201694720081796846702960249688144417680786846465
 278162906898013748642772019172998608839057854602841254854175736240572851175099616062424065
 2963658210542356083852877246926416492931527804540089510269883905
 1692492088492238622532768569558090666689925078386295740708067178336619326186090793391105
 644811775887535379664225513644980219319376317839497786625735944865592422785
 2845358328636614328617082131255054540223949221002124433109986305
 74875990602425226938138664024259158432269224416705
 1018329989576989704159754753835889677652405111555820545
 71967245196653338257378864734797608168672816153312963139871238665985
 19666546275088335320957353962363201658812107005039715284928928608628170883585
 129959381219943649417033775959204959948797179242551459265680758859265
 463149379463251167706230703520995680069543921166639491398457345
 19948738964527549499432007591778845447137932958457586625953063419475941273954097665
 165502573617193579886078524884554371013787876466850820614145
 382314270322310985139418831028955559235551077239363319937510690579825910692881422216705
 2853450403236152332571821875265293508017495635204070217869999840422343584089739265
 14701083488299057530174696885922722686956286485260401577115414785
 61751285336040585295804391670071058142224865543324607243406589162503580666870926270465
 37839385943068863406967633413004957540054532539686888463944906014566240419460804270776358938980032660929917901837033235462145
 772459017179480479061611372132330246001039753130436193419524315193543873326133868681083905
 321030150905393790929751720043602006651739765349595158023943724894346115208705
]

var bern = Hash(
1 0
2 1
3 2
4 4
5 6
6 10
7 12
8 30
9 36
10 60
11 72
12 108
13 120
14 144
15 180
16 240
17 360
18 420
19 540
20 840
21 1008
22 1080
23 1200
24 1260
25 1620
26 1680
27 2016
28 2160
29 2520
30 3360
31 3780
32 5040
33 6480
34 7560
35 8400
36 10080
37 12600
38 15120
39 25200
40 30240
41 42840
42 45360
43 55440
44 60480
45 75600
46 85680
47 100800
48 110880
49 128520
50 131040
51 166320
52 196560
53 257040
54 332640
55 393120
56 514080
57 655200
58 665280
59 786240
60 831600
61 917280
62 982800
63 1081080
64 1179360
65 1285200
66 1310400
67 1441440
68 1663200
69 1965600
70 2162160
71 2751840
72 2827440
73 3326400
74 3341520
75 3603600
76 3931200
77 4324320
78 5654880
79 6652800
80 6683040
81 7207200
82 8648640
83 10810800
84 12972960
85 14414400
86 18378360
87 21621600
88 36756720
89 43243200
90 64864800).values.sort

var nf = [80, 120, 144, 2520, 5760, 6480, 7920, 15120, 30240, 94248, 110880, 285120, 597168, 604800, 1441440, 1663200, 1738800, 2217600, 5216400, 13305600, 43243200, 64864800, 648648000, 4034016000, 8951342400, 12070749600, 67541947200]

#say arr.join(' ')

#var primes = [3, 5, 17, 23, 29, 53, 83, 89, 113, 197, 353, 617]
#var primes = [3, 5, 17, 23, 29, 53, 83, 89, 113]
var primes = [3, 5, 17, 23, 29, 83]
#var primes = [3, 5, 17, 23, 29, 43, 53, 89, 113, 127, 157, 257]

var P = primes.prod

for n in (arr) {

    say "# n = #{n.len}"
    var f = n.factor.grep { !primes.has(_) }

    for k in (f.len ^.. f.len-5 ) {
        say "# Combination: #{k}"
        f.combinations(k, {|*a|
          with (a.prod * P) {|c|
              if (c.is_carmichael) {
                say "\n\t\t\tFound: #{c}\n"
            }
          }
        })
    }
}

__END__
for n in (arr.map{.lambda}.uniq.sort) {
    say "# Bern = #{n}"
    var d = n.divisors.grep{ _ > 1}.map{.inc}.grep{.is_prime}.grep{!primes.has(_)}.grep{ _ > primes.max}.grep{ _ < 1e6}

    for k in (1..d.len) {
        say "# Combination: #{k}"
        d.combinations(k, {|*a|
                with (a.prod * P) {|c|
                    if (c.is_carmichael) {
                    say "\n\t\t\tFound: #{c}\n"
                    }
                   #say c if c.is_pseudoprime
                }
        })
    }
}